Warning: this video from TEDEd might make your head hurt - it gets into the mathematical reasoning behind the idea of infinity, and then goes one step further and explains why there are actually an infinity of infinities out there. Heavy ideas. But the video is also a great reminder of the possibilities of mathematics, as well as its limitations.

As the narrator, software developer and former mathematics professor Dennis Wildfogel, says, "if these ideas make you uncomfortable, you're not alone". They're the same ideas that led the guy who discovered them, Georg Cantor, to spend the second half of his life in and out of mental institutions. But that had more to do with unfriendly mathematical colleagues who cast doubt on his theories, so you should be able to watch and learn safely:

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